JP2002055605A - Public key ciphering and deciphering method and system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a new public key ciphering and deciphering method and its system, in which a knapsack problem is made the basis for safety. SOLUTION: A prime number (p), a mutually prime progression p1,..., pn} and a generation origin (g) are generated. Then, a1,..., an which satisfy pi≡gai (mod p) are obtained. Then, random numbers (d) are generated, and a public key bi=(ai+d)mod(p-1) is obtained. Then, for a ciphering process, a plain sentence M is converted into a binary string m=(m1, m2,..., mn), having a length (n) and a Hamming weight (k) and a ciphering sentence (c); shown by Equation (1), is generated. Then, r=c-kd(mod(p-1)) is generated from the sentence (c), and u=gr (mod p) is obtained. When pi is a factor of (u), let mi=1 to generate the binary string m=(m1, m2,..., mn); and when pi is not a factor of (u), by letting mi=0 to generate the binary string (m), the string (m) is converted back into the sentence M.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a public key encryption / decryption method and system, and more particularly to a public key encryption / decryption method and system which take the knapsack problem into account.

[0002]

BACKGROUND OF THE INVENTION Public key cryptosystems are categorized by their security concerns. Examples of such problems include a prime factorization problem, a discrete logarithm problem, and a knapsack problem. Among these problems, there are Markle-Hellman (Markle-Hellman) and Chor-Rivest (Call-Revest) ciphers as public key cryptosystems that rely on the knapsack problem for security. Even successful attacks have been reported.

[0003]

SUMMARY OF THE INVENTION The present invention realizes a new public key encryption / decryption method and system which takes the knapsack problem as a source of security.

[0004]

According to the present invention, a key generation process is performed by using a discrete logarithm problem on a rational integer ring, and a length is calculated.

[0005]

(Equation 13)

[0006] Hamming weight with integer and length n
We show a new method of performing encryption and decryption using conversion with a binary sequence of k.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a construction method of a public key cryptosystem used in the present invention will be described with reference to FIGS. 1, 2, and 3. FIG. (Key generation processing: FIG. 1) The key generation processing unit includes a random number generator A (1
01), a discrete logarithmic calculator (102), a random number generator B (103), and an adder A (104). (1) Let the sizes of the vectors be integers n and k, respectively (n,
k is made public. ), The n and k inputs, vector using a random number generator _{A (101) {p 1,} p 2, ···, p n} any subset from {p _i1, p _i2, ··・, P _ik ｝

[0008]

[Equation 14]

A prime number p that satisfies, a prime number p that is relatively prime
₁ , p ₂ ,..., P _n ∈Z / pZ (a field of integers modulo the prime number p) and a generator g of the group (Z / pZ) are generated. (2) Next, p ₁ , p ₂ , ..., p generated by the random number generator A (101)
Input _n and g, and use a discrete logarithmic calculator (102)
A ₁ that satisfies p _i ≡g ^ai (mod p) for ≦ i ≦ n
・ Calculate a, _n . (3) Further, an integer d from Z / (p-1) Z is generated by using a random number generator B (103). (4) Finally, p generated by the random number generator A (101), a ₁ ,..., A _n generated by the discrete logarithmic calculator (102), and p generated by the random number generator B (103) Is input, and using the adder A (104), the public key b _i = (a _i + d) mod (p−
Output 1). (Encryption processing: FIG. 2) The encryption processing unit is a plaintext converter (20
1) It comprises an adder B (202).

[0010] Length

(Equation 15)

(1) Plaintext M, n and k are input, and plaintext converter (20
Using 1), let M be a binary sequence m = length n and Hamming weight k
(m ₁ , m ₂ ,..., m _n ). (2) Enter the public key b _i determined in m and the key generation processing unit which has been converted in the clear converter (201), using an adder B (202), the ciphertext

[0012]

(Equation 16)

Is generated and output. (Decoding processing: FIG. 3) The decoding processing unit includes a subtractor (301), a power operator (302), a factor checker (303), and an intermediate decoded text converter.
(304). (1) Input the ciphertext c and the secret keys d, p, and k, and obtain r = (c−kd) mod (p−1) from the ciphertext c using the subtractor (301). (2) Next, g generated by the random number generator A (101) and a subtractor (30
The r obtained in 1) is input, and u = g ^r (mod p) is generated from r using a power calculator (302). (3) Further, p ₁ , p ₂ ,... Generated by the random number generator A (101)
·, _Pn and u generated by the power calculator (302) are input, and using a factor checker (303), a binary sequence m = (m ₁ , m ₂ ,..., m _n ), and if p _i is a factor of u, m _i = 1
If it is not a factor, it is determined by setting m _i = 0. (4) Finally, input n, k and m obtained by the factor checker (303),
M is converted to plaintext M using the intermediate compound sentence converter (304).

[0014]

The public key cryptosystem realized by the present invention utilizes a discrete logarithm problem on a rational integer ring in a key generation process, and p, p ₁ ,..., _Pn , g, d By keeping the secret, it is possible to withstand an attack for directly obtaining a secret key from a public key. In encryption and decryption,

[0015]

[Equation 17]

By utilizing the conversion between an integer of length and a binary sequence having a length n and a Hamming weight k, the density, which is a security index of a knapsack cipher, can be sufficiently increased. Low-de to obtain ciphertext directly from plaintext
Resists nsity attacks. A formal description of safety is given in the literature (T. Okamoto, K. Tanaka, S. Uchiyam
a, ”Quantum Public-Key Cryptsystems”, Proc.of C
RYPTO2000, Springer, 2000).

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a key generation processing unit.

FIG. 2 is a block diagram illustrating a configuration of an encryption processing unit.

FIG. 3 is a block diagram showing a configuration of a decoding processing unit.

[Explanation of symbols]

 101 random number generator A 102 discrete logarithmic calculator 103 random number generator B 104 adder A 201 plaintext converter 202 adder B 301 subtractor 302 power operator 303 factor checker 304 intermediate decoded text converter

 ────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Shigenori Uchiyama 2-3-1 Otemachi, Chiyoda-ku, Tokyo F-term (reference) in Nippon Telegraph and Telephone Corporation 5J104 JA23 JA29 JA30 NA17

Claims (6)

[Claims] A key generation processing unit, an encryption processing unit, and a decryption processing unit, where n and k are integers, a prime number p and a mutually prime sequence {p ₁ ,.・, P _n ｝, generator g
Generates, a ₁ which satisfies p _i ≡g ^ai (mod p) for each 1 ≦ i ≦ n, · · ·, seeking a _n, generates a random number d, each 1 ≦ i A public key b _i = (a _i + d) mod (p−1) is obtained for ≦ n, and the length of the encryption processing unit is Where M is the plaintext of m, a binary sequence m = (m ₁ , m ₂ ,..., Where M is a length n and a Hamming weight k
·, M _n ), and the ciphertext The decryption processing unit generates r = (c−kd) mod (p−1) from the ciphertext c, obtains u = g ^r (mod p), and obtains the length n and the Hamming weight k. Some binary sequence m = (m ₁ , m ₂ , ..., m
_n ) is generated by setting m _i = 1 if p _i is a factor of u, and by setting m _i = 0 if p _i is not a factor, and converting m into plaintext M. Method. 2. A key generation processing unit comprising: a key generation processing unit and an encryption processing unit, where n and k are integers, and a prime number p and a mutually prime sequence ｛p _{1 ,.} ｝, Generator g
Generates, a ₁ which satisfies p _i ≡g ^ai (mod p) for each 1 ≦ i ≦ n, · · ·, seeking a _n, generates a random number d, each 1 ≦ i A public key b _i = (a _i + d) mod (p−1) is obtained for ≦ n. When the plaintext was M, binary sequence m = a M length n is a Hamming weight _{k (m 1, m 2,} ···, m n) into a ciphertext Equation 4] Generating an encryption method. 3. A key generation process, where n and k are integers, a prime number p, a mutually prime sequence {p ₁ ,..., P _n }, and a generator g
Generates, a ₁ which satisfies p _i ≡g ^ai (mod p) for each 1 ≦ i ≦ n, · · ·, seeking a _n, generates a random number d, each 1 ≦ i A public key b _i = (a _i + d) mod (p−1) is obtained for ≦ n, and the length is expressed as When the plaintext was M, binary sequence m = a M length n is a Hamming weight _{k (m 1, m 2,} ···, m n) is converted into the ciphertext [6] The decryption unit generates r = (c−kd) mod (p−1) from the cipher text c, and u = g ^r (mod p ), And a binary sequence m = (m ₁ , m ₂ ,..., M having a length n and a Hamming weight k
_n ) is generated by setting m _i = 1 if p _i is a factor of u, and by setting m _i = 0 if p _i is not a factor, and converting m into plaintext M. 4. As a key generation process, when n and k are integers, a prime number p, a mutually prime sequence {p ₁ ,..., P _n }, a generator g
A random number generator A for generating a a ₁ which satisfies p for each ^{_{1 ≦ i ≦ n i ≡g ai}} (mod p), ···, seeking a _n discrete logarithm calculator, a random number a random number generator B for generating d, an adder A for obtaining a public key b _i = (a _i + d) mod (p−1) for each 1 ≦ i ≦ n, Equation 7 Where M is the plaintext of m, a binary sequence m = (m ₁ , m ₂ ,..., Where M is a length n and a Hamming weight k
·, M _n ) and a ciphertext , A subtractor for generating r = (c−kd) mod (p−1) from the ciphertext c as a decryption process, and a power operation unit for obtaining u = g ^r (mod p) And a binary sequence m = (m ₁ , m ₂ ,..., M having a length n and a Hamming weight k
_n ) is provided with a factor checker that generates m _i = 1 if p _i is a factor of u and m _i = 0 if p _i is not a factor, and an intermediate decoding converter that converts m into plaintext M. A public key encryption / decryption system. 5. In the key generation processing, when n and k are integers, a prime number p, a mutually prime sequence {p ₁ ,..., P _n }, a generator g
A random number generator A for generating a a ₁ that satisfies the public for each 1 ≦ i ≦ n key ^{_{p i ≡g ai (mod p)}} , ···, seeking a _n discrete logarithm calculator A random number generator B for generating a random number d; an adder A for obtaining a public key b _i = (a _i + d) mod (p−1) for each 1 ≦ i ≦ n; , Length [Equation 9] When the plaintext was M, and the plaintext converter for converting M is a Hamming weight k with length n binary sequence _{m = (m 1, m 2} , ···, m n) , the ciphertext [ Equation 10 An encryption device comprising: an adder B that generates. 6. A key generation process, where n and k are integers, a prime number p, a mutually prime sequence {p ₁ ,..., P _n }, and a generator g
A random number generator A for generating a a ₁ which satisfies p for each ^{_{1 ≦ i ≦ n i ≡g ai}} (mod p), ···, seeking a _n discrete logarithm calculator, a random number a random number generator B for generating d; an adder A for obtaining a public key b _i = (a _i + d) mod (p−1) for each 1 ≦ i ≦ n; When the plaintext was M, and the plaintext converter for converting M is a Hamming weight k with length n binary sequence _{m = (m 1, m 2} , ···, m n) , the ciphertext [ Equation 12 A ciphertext c generated by an encryption device having an adder B for generating the following, and as a decryption process, a subtractor for generating r = (c−kd) mod (p−1) from the ciphertext c. , U = g ^r (mod p), and a binary sequence m = (m ₁ , m ₂ ,..., M having a length n and a Hamming weight k
_n ) is a factor checker generated by setting m _i = 1 if p _i is a factor of u, and m _i = 0 if p _i is not a factor, and an intermediate decoded text converter for converting m to plain text M. A public key decryption device comprising: